If you flip a coin and roll a $6$ -sided die, what is the probability that you will flip a heads and roll less than a $6$ ?
Solution: Flipping a heads and rolling less than a $6$ are independent events: they don't affect each other. So, to get the probability of both happening, we just need to multiply the probability of one by the probability of the other. The probability of flipping a heads is $\dfrac{1}{2}$. The probability of rolling less than a $6$ is $\dfrac{5}{6}$, since there are $5$ outcomes which satisfy our condition (namely, $1, 2, 3, 4,$ and $5$ ), and $6$ total possible outcomes. So, the probability of both these events happening is $\dfrac{1}{2} \cdot \dfrac{5}{6} = \dfrac{5}{12}$.